Measurement of visual range in fog

ABSTRACT

Apparatus for measuring visual range in fog comprises a transmitter which transmits a pulsed parallel beam of radiation, a receiver which measures the radiation reflected by the fog, and means for integrating the received brightness with respect to time. A measure of the visibility is derived from the integrated brightness.

United States Patent Noxon 1 Mar. 21, 1972 [54] MEASUREMENT OF VISUALRANGE IN [56] References Cited EGG UNITED STATES PATENTS 1 lnvemorl PaulAdelbe" Now", Tenaflw 3,175,214 3/1965 Ramsay et a1 .343/13 [73]Assignee'. Thorn-Bendix Limited, New Barnet, He 3,316,548 4/1967 DArmco..343/1l7 fordshire, E g 3,510,225 COHIS 3,419,333 12/1968 Towner.....[22] F11ed: Sept. 10, 1969 3,428,814 2/1969 Doonan.... [2H App} No, 856565 3,146,293 8/1964 Lesage ..356/205 Primary Examiner-Rodney D.Bennett, Jr. [30] Foreign'Application Priority/"Data AssistantExaminerS. C.'Buczinski t P l k Sept. 13, 1968 Great Britain ..43,78l/68A 'omey Kemon a men? Estabmo [57] ABSTRACT [52] [1.8. CI ..356/4,356/205, 343/5 LS,

343/5 w Apparatus for measuring visual range in fog comprises a trans-51 1111.01. ..G0lc 3/08, 00111 21/22 miner which transmits a Pulsedparallel beam of radiation, 3 [58] Field of Search 343/5 GC, 5 W, 117,13, 5 LS; receiver which measures the radiation reflected by the fog, 354 205 and means for integrating the received brightness with respect totime. A measure of the visibility is derived from the integratedbrightness.

13 Claims, 6 Drawing Figures Xc0s AMP

1 P1255151 R FLHZZZIM-I/ 27 ZZLIMK "2o 1 r 1 I CAT-E 1, INZEGRATOR 1, RhX corvmotlj 6,

1* (w X(F06) 30 29 SEA xmron sou/1mm rrsszr Patented March 21, 19723,650,627

5 Sheets-Sheet 1 M0 70 -MUL M 1 [2 Patented March 21, 1972 3,650,527

5 Sheets-Sheet 2 P512551 L/M-I) ZZLIMK I t l GATE t; GATE INTEEGRATOR Lf0 Ipdt m x F CONTROL j 561 Z; 28 (wt X(FOG) 30 29 56A xmwn EQUATIONPatented March 21, 19 72 3,650,612 7 5 Sheets-Sheet 4 GATE TE CONTROL TEx INTERROGATE I R (t!) Lia!) PRESET Jin /7:171:

MEASUREMENT 01F VISUAL RANGE IN FOG The present invention relates to themeasurement of visual range in fog and is applicable especially to theprovision of information for use by pilots when landing on airfieldrunways in fog.

The equipment at present in use for measurement of fog density onairfields comprises a standard light source and a receiver spaced fromthe source which measures the light received from the source andcompares it with the light which would be received in the absence offog. This equipment only gives a measure of visual range at runwaylevel. To elevate the source and receiver above the runway would beunacceptable because they would then occupy airspace required by theaircraft. Some work has been done on the use of back scatter from atransmitted beam of radiation to determine fog density (see BackscatterSignature Studies for Horizontal and Slant Range Visibility, SperryRand' Research'Center, Sudbury, Massachusetts, United States of America,May 1967) but so far without much success.

The present invention arises from an analysis of the factors governingvisibility in fog. In what follows the following references will bereferred to by number:

1. Backscatter Signature Studies for Horizontal and Slant RangeVisibility Sperry Rand Research Center, Sudbury, Massachusetts May i967.

2. Contrast Thresholds of the Human Eye" Blackwell, Journal oftheOptical Society ofAmerica Nov. 1946.

3. Theory of Fog Simulation P.A. Noxon, Engineering Report, Feb. 26,1968 The Bendix Corporation. Navigation and Control Division, Teterboro,New Jersey, United States of America.

4. A Method for Creating a Fog Illusion for ln-Flight Training" P.A.Noxon, AIAA Paper, June 1967.

it is generally recognized that ones ability to see a given objectdepends on three parameters: (1) the angular size of the object, (2) theadaptation brightness, and (3) the contrast ratio (defined as thedifference in brightness between the object and its background dividedby the background brightness). This matter is covered in detail inReference No. 2.

The presence of fog in the line of sight affects both the apparentbrightness of the object, by attenuation, and the brightness of thebackground by the reflection of daylight and other ambient light by thefog particles (the backscatter).

ln Reference No. 3, there is developed an equation covering therelationship of the parameters in daylight. (Equation 23 of ReferenceNo. 3). This equation is as follows:

V: Ive-IA oQ-l- (1) where V= contrast ratio 1,,= ambient light value Ibrightness ofobject (assumed to be self-luminous) Q albedo orreflectance coefficient of terrain surrounding object (e.g., grass) F=albedo or reflectance of fog x distance in feet along line of sightbetween eye and object a fog density coefficient As previouslymentioned, the liminal or extinction value of V depends on object size,and adaptation brightness (probably closely represented by 1,, inEquation (1) it is probably not really known what this liminal value isfor the pilots situation. He is not concerned with recognizing a singleknown object under test condition, but rather deriving reliable guidancefrom a visual scene. This must be studied further, of course, but we canonly assume that for a given airfield, some definite value exists at agiven value of I which can be measured. This specific value of V mustalso inescapably include the local pertinent values of Q, as well as thearrangement and relative brightness ofthe runway lights.

The fog density coefficient a, which appears both in attenuation andbackscatter computations (see Equations (4) and (5) in Reference No. 3)represents the equivalent projected area of the fog particles per unitarea per lineal foot along the line of sight. While only a homogeneousfog structure was considered in Reference No. 3. where a would be aconstant, a more flexible treatment is possible. (See Reference No. 4.)in that paper, it was shown that one could assume a to be some functionof x such as a =f(x). The integration involved in solving the basicdifferential equation can then be indicated instead of completed, inwhich case the term ax= fflrldn Equation l then becomes:

7 be n I Q+I F(f l) It is not necessary, then, to know the details ofthe fog structure along the line of sight to evaluate any of the fogequations, including (2) above, but only the value of the total integralff($)dx.

This is a basic principle which we shall employ in the system to bedescribed.

COMPUTATION FOR LlMlNAL VALUE OF fffw) dz.

Solving Equation (2) for ej'fixhix VI0Q+ VI0Fef "VI0F=IoQ IA 1 IA) Q fl-VF 10 F (3 For any given situation, all quantities on the right-handside of Equation (3) are known or can be directly measured, thus aliminal value of fftrhi:

and hence can be determined. Let us lump these terms and assign Z,,,,,to represent them zum= r 01 W ff(:z:)ala:=log, Z (4) This is the valueof f f (:c)dx

which provides extinction for that particular airport, condition ofambient light, etc.; and it is the task of the fog-measuring elementofthe system to evaluate this term.

It will be shown in what follows that f f (:c)d:v

V is a function of the brightness at the receiver integrat ed withrespect to time after transmission of a short pulse. Moreover, it ispossible to determineflx) from the instantaneous value of the brightnessand the integrated brightness at a time corresponding to travel of thepulse to a distance x and back. Thus visual range can be obtained eitherdirectly from the integrated brightness or indirectly by integrating thefog density f(x) along the line of sight.

In accordance with the invention, therefore, there is provided apparatusfor measuring visual range in fog comprising a transmitter fortransmitting a pulsed parallel beam of radiation, a receiver formeasuring the radiation reflected back along the same path by the fog,means for integrating the received brightness with respect to time, andmeans for deriving from the integrated brightness a measure ofvisibility.

The means for deriving a measure of visibility may comprise means fordetermining the time taken after transmission of a pulse for theintegrated brightness to reach a set level. The visual range is thenrepresented by half the distance travelled by the measuring radiation inthe said time.

The set level is a function ofa number of parameters, some of which areconstant for a given location and some of which vary with fog conditionsand have to be separately measured. These parameters are the extinctionvalue of the contrast ratio V, the albedo or reflectance coefficient Qof the terrain surrounding an object, the albedo F of the fog, thebrightness I of the object, the ambient light value I,,, the albedo ofthe fog for the measuring radiation F,,,, the brightness 1 of thetransmitter, and the pulse length vp. The extinction value of V, that isto say the value at which the object is no longer visible to theobserver, is dependent on the size of the object and the adaptation ofthe observer's eye to ambient light. In the application of the inventionto measurement of fog conditions on airfield runways it will also benecessary to take into account the fact that the aircraft pilot wishesto be able not merely to see a test object but to derive reliableguidance from the objects he is able to see on the ground. For thisreason the effective extinction value of V may be higher. Under anygiven ambient light conditions an appropriate extinction value of V canbe set into the equipment, if necessary by the use of empiricallydetermined values.

Alternatively the means for deriving a measure of visibility maycomprise means for calculating the fog density f(x) at various distancesx from the instantaneous values of the brightness and the integratedbrightness at a time corresponding to the receipt of reflected radiationfrom the distance x. When the fog density has been determined in threedimensions by the use of several transmitter/receiver units the visualrange can be determined by the apparatus for any given line ofobservation by computing and comparing it with the limiting value log,.Zwhich is dependent on the parameters set out above.

The radiation beam may have whatever frequency is most convenient in anyparticular case. As an example, the present specification will describeapparatus using light generated by a laser since this facilitates theproduction ofa collimated beam, but it may also be possible, forinstance, to use a radar beam.

The use ofa beam of white light for measu ement is desirable since thiscorresponds more accurately with the actual conditions of observationthan the use of radiation at a single I vt/2 where t is time of arrivalof reflected pulse I-,= brightness of transmitter 1 brightness at fogelement 1 brightness at fog element after reflection 5 brightness atreceiver F albedo or reflectance of fog for the measuring radiation f(xfog density coefficient Now:

f(x)dx t t dt I =I e f =I e (5 2 l mf( l) p V f -t dt I F 2 IT vpe f 21f(x)dx r t at I =I e f I =I e f 2 -2 r t dx I =I F vpe f(% t)- This isinstantaneous received pulse amplitude. Let Ln=time integral of return,or H 25 t R olndt Fm] -z r t dt L 2 [(2 I)! 2 L L M t *I GO v M f('2)) Ve2f1( t dt=1 I 2IL 1 40 but T 111 1 we can equate the RH. sides ofEquations 4 and l3 thus:

frequency. The pulses should be very short, with a length of the orderof 10 nano-seconds.

We shall now show the relationship between and the time integral of thereceived brightness for a system using a collimated beam fortransmission and reception, taking into account only a single reflectionfrom the fog particles. Let:

v velocity oflight t= time p pulse length vp= pulse length x, distancealong collimated beam or more simply, since I and vp are constants forthe system The terms on the right-hand side of Equation l 5) are eitherconstants for the particular situation or else measurable parameters andcan thus be set into the apparatus. When L reaches the value representedby the Equation IS) The time I over which the received brightness hasbeen integrated represents the time for light to travel to the limit ofthe visual range and return and is thus a direct measure of the visualrange.

The apparatus can include a gate adjustable to operate at differenttimes relative to the transmitted pulse to cut off the return signalwhen the integrated brightness reaches the set level. The gate isconveniently controlled by a difference signal derived from comparingthe integrated brightness with the set level, the latter being subjectto variation as ambient light and other conditions change. The time ofoperation of the gate then continuously represents the visual range. V

The apparatus is set up on the ground and can measure the visual rangein whatever direction it is pointing. On an airfield it is required topredict what will be the runway visual range, that is to say thedistance the pilot can see along the runway, for various altitudes ofthe aircraft on the glide slope. If the visual range 1: is measured bythe apparatus when inclined upwards at an angle (1: then an aircrafthaving these co-ordinates relative to the apparatus will just be able tosee the part of the runway where the apparatus is situated. The aircraftaltitude h is equal to 1: sin ti: and the runway visual range V.R. isequal to x cos 8. Ifthe aircraft is on a glide slope of angle whichintersects the runway at a point distance D from the apparatus it can beshown that x= (D tan 0)/(sin d) tan 0 cos 4)).

By varying 4; this equality can be satisfied for the measured value ofxand h and V.R. can be determined by resolving x.

Thus by installing a number of sets of such apparatus at intervals alongthe runway information can be obtained of the altitude and visual rangeat various points along the glide slope.

Practical embodiments of the invention are shown in the drawings, inwhich FIG. I is a diagram ofa transmitter/receiver unit,

FIG. 2 shows the mounting of the transmitter/receiver unit and a blockcircuit diagram ofa data processer for determining aircraft altitude hand runway visual range V.R.,

FIG. 3 is a diagram illustrating the use of a vertically directedtransmitter/receiver unit and resolution along the line of sight in astratified fog,

FIG. 4 is a block diagram of a data processer employing the resolutiontechnique illustrated by FIG. 3, and

FIG. 5 is a block diagram of a data processer for determiningf(x) FIG. 6is a logic diagram for calculating the runway visual range V.R. atvarious heights H on a glide path.

In the unit shown in FIG. 1 a laser 10 generates a pulsed beam which isformed by a mirror 11 and lenses 12 and 13 into a broad parallel beamwhich is transmitted into the fog. A beam splitter 14 is positioned toreceive radiation reflected back along the transmission path and todirect this radiation by way of a lens 15 onto a photomultiplier 16whose output is applied to the data processer.

In FIG. 2 the unit of FIG. 1 is shown at 17 and is mounted on ahorizontal shaft 18 carried by trunnions (not shown). The shaft 18 isrotatable through gearing 19 by means of a motor 20 which receives aninput from a servo amplifier 21 and adjusts the angular position of theunit 17 accordingly. This angular position (b is measured by atransducer 22 on the shaft 18 which supplies a signal representing 15 tothe data processer. The latter also receives the output I of the photomultiplier 16 of the unit 17. A resolver 23 on the shaft 18 receives asignal representing 2: and generates x cos V.R. and x sin 4) h.

The data processer includes a gate 24 through which the signal I passesto an integrator 25. The output L of the integrator is compared with bya comparator 26 and the resulting difference signal is applied by a gatecontrol circuit 27 to close the gate 24 when the difference falls tozero. The gate control circuit supplies a signal 1, representing thetime of gate closure, to a multiplier circuit 28 generating an outputrepresenting visual range x (lg/2) along the line of sight of thetransmitter/receiver unit A circuit 29 calculates a value ofx byEquation (16) from preset values of D and 0 and the instantaneous valueof from the transducer 22. A comparator 30 derives a difference signalfrom the outputs of the two circuits 28 and 29, which is applied throughthe amplifier 21 to the motor 20 to adjust until the value ofrepresenting the visual range from the unit 17 corresponds with thegeometrical conditions for an aircraft on a particular glide path. Theoutputs of the resolver 23 then give an altitude of the aircraft and acorresponding' runway visual range.

To obtain information on visual range at a fixed altitude. theexpression x h/sin (b replaces Equation (16) and the block circuit forgenerating x from the geometrical conditions is modified to handle apreset input 11 in place of D and 6. By changing h sequentiallyinformation can be gathered over a range of altitudes.

1n the system which we have described so far, the assumption has beenmade that the radiant energy used for measurement be directed along thepilot's line of sight. It would thus strike directly into his eyes, ifhe happened to look in the direction of the ground equipment at themoment it was searching his altitude. While this would be tolerable if anonhazardous part of the spectrum, such as K-band, be employed, it wouldplace serious restriction on the use of visible light, which might bedesirable for other reasons, since a laser sufficiently powerful topenetrate the required distance could in some circumstances destroy hiseyesight.

There is, fortunately, a possibility of mitigating these difficulties,by directing the measuring beam straight upward at all times, andemploying resolution techniques to obtain the required data. Thisorientation of the beam is much less hazardous, since it is almostimpossible in normal circumstances to loolt straight down from anairplane.

For this purpose, we must assume that while the fog can have randomstructure vertically, it is laterally isotropic; i.e., perfectlystratified. Such a structure is, in fact, well approximated at times innature, especially during conditions of low fog. Consider FIG. 3.

Consistent with our previous nomenclature, x, is the distance along theline ofmeasurement, in this case vertically, and x is the distance alongthe line of sight. Let the vertical structure be random, such that, aspreviously considered, we

let a, the density coefficient, be a function ofx or Now x=( r)l (sin(18) According to our assimptions, the ragaefisn coefficient a is thesame for each corresponding point on x, and x, thus the respective areaelements will be proportional to the above ratio.

We are therefore at liberty to take our measurements in a verticaldirection and resolve to the pilots line of sight. To the degree thatthe fog departs from an isotropic structure, the result will, of course,be in error. Since, as mentioned previously, many fogs approximate thisform, and in any case a number of measuring elements, distributed aboutthe area, will be employed, it seems a worthwhile trade-off to take inview the many advantages associated with this arrangement. We shouldinclude the fact that since the measuring light will, in general, travela shorter distance, a smaller amount of power may suffice conversely, atthe same power level. better resolution can be had. Now Equation 17)states that:

x (x,)/(sin qb). Also Equation (22):

1 sin fron s.-

loge =sin log, lim

tinuously recom pute the li minal valuegf j by mean of Equation (26).Eventually, a point will be found where the measured value of L and thecomputed value for the value of (b involved will be equalfAlso, Han'iiTJiiiifiii'efiB $653 out as before.

Suitable apparatus for effecting the computation is shown in FIG. 4,which is a schematic drawing similar to FIG. 2 but with themodifications necessary for effecting resolution of the measurementsonto a line of observation at an angle (1) to the horizontal.

Parts corresponding to those of FIG. 2 are given the same referencenumerals and will not be further described. The unit 17 is no longerswingably mounted but is fixed to look vertically upwards. The output ofthe comparator 30 is therefore not applied to control the position ofthe unit 17 but is applied to an integrator 31 which generates a signalrepresenting the angle d). This signal forms the input to the circuit 29which in FIG. 2 was derived from the transducer 22. It also forms oneinput ofa logic unit 32 which computes for comparison in the comparator26 with the measured value of L The value of d) is automaticallyadjusted unti it complies with th e geo metr ical cdnditidnsfifiiii'fiifiiiiafi' and runway visual range V.R. are then given by logic units33 and 34, respectively, which compute x sin 5 and x cos 5,respectively.

The apparatus of FIG. 4 can be modified in a similar manner to that ofFIG. 2 to provide measurements at set altitudes. As

before a number of such apparatus would be distributed about theairfield to build up a three-dimensional picture of the fog conditionslikely to be encountered by a pilot during landing.

it will now be shown that the transmitter/receiver unit 17 can be usedto determine actual values of the fog density f(x) and thus by use ofseveral units distributed over the airfield and directed vertically itis possible to build up a mapof the fog density distribution in threedimensions. As a result it is not necessary to rely'on assumptions as tothe stratification of the fog in computing visual ranges since f2ficanbe computed for any line of sight.

For this purpose we write Equation (8) above in terms of distance x:

Thus the fog density at a distance x from the transmitter/receiver unitis determinable from the received brightness at the instantcorresponding to receipt of radiation reflected from that distance andthe integrated value L of that brightness at the same instant. Bydetermination off(x) for various distances it is possible to build up apicture of the vertical distribution of fog density above a verticallydirected transmitter/receiver unit. Thus by the use of an array ofvertically directed units the overall fog distribution can bedetermined.

FIG. 5 shows the data processer associated with one of an array of unitswhich are connected to a central computer which by interrogation obtainsvalues of f(x) from the various units to build up the overalldistribution. The output I from the unit 17, as before, passes throughthe gate 24 to the integrator 25. The gate is controlled by the gatecontrol circuit 27 which in this case receives interrogation signalsfrom the central computer representing a particular value of x. The gateis accordingly closed at the corresponding instant I, to give a value ofL (t,) at the output of the integrator 25 and a value of I (t at theoutput of the gate 24. These are passed to a logic unit 35 which alsoreceives preset values of I vp, and F,,, and computesflx) fortransmission to the computer. i

The data can be processed in various ways by the computer in order toobtain runway visual range for any position of an aircraft. lt ispossible, for example, for the computer to store data representative ofthe fog density distribution from which can be obtained for any givenline of sight. Then for any given height on a particular glide path canbe calculated for lines of sight at various angles and compared withlog,.Z,,,,, to find the runway visual range.

By way of example FIG. 6 shows a logic diagram for a computer forcalculating the runway visual range V.R. at various heights H on a glidepath from information as to fog density received from a number of unitsspaced at equal intervals along the ground below the glide path. Theoutputs of the various units are represented byf (x) ,j"; (x) ..f,, (x).Distance along the ground is represented by R and the distance betweenunits by A R. The integrated fog density in a horizontal direction isapproximated to by the expression This is obtained by means of aninterpolator 36 and an integrator 37. It is then resolved to the line ofsight by multiplying by l/sin A in the block 38, the angle A being thatbetween the chosen line of sight and the vertical. The output from 38 isapplied to a difference circuit 39 which also receives log Z andgenerates a difference signal which is applied to a circuit 40 to adjustA until the difference is reduced to zero. The output from 40representing the angle A, in addition to being supplied to the block 38is fed to a second multiplier 41 to convert an input height H into thecorresponding runway visual range V.R. for the prevailing fog densityconditions.

What l claim is:

1. Apparatus for measuring visual range in fog comprising:

a transmitter for transmitting a pulsed parallel beam of radiation;

:1 receiver for measuring the radiation reflected back along the samepath by the fog;

means for determining the mathematical integral of the receivedbrightness at any instant over a time period which period is of theorder of several times the pulse length; and

means for deriving from the integrated brightness a measureofvisibility.

2. Apparatus as claimed in claim 1 wherein the means for deriving ameasure of visibility comprise means for determining the time takenafter transmission of a pulse for the integrated brightness to reach aset level.

3. Apparatus as claimed in claim 2 having a gate coupling theintegrating means to the receiver, a gate control circuit, and acomparator comparing the output of the integrating means with the setlevel and supplying a difference signal to the gate control circuitwhereby the control circuit closes the gate when the set level isreached and generates an output representing the time of gate closure.

4. Apparatus as claimed in claim 3 including a second comparator whichcompares the output of the gate control circuit with a reference signalfrom a reference circuit which is a function of aircraft position and ofthe elevation angle d of the line ofobservation, the output ofthe secondcomparator being applied to vary d until the line of observationcoincides with the line of sight of the aircraft.

5. Apparatus as claimed in claim 4 in which the transmitter/receiverunit is swingable about a horizontal axis by a servomotor to adjust theangle of elevation, the output of the second comparator being applied tothe servomotor.

6. Apparatus as claimed in claim 2 which the transmitter/receiver unitis mounted to observe in a vertical direction and the set level is afunction of the angle of elevation :13 of a desired line of observation.

7. Apparatus as claimed in claim 4 in which the transmitter/receiverunit is mounted to observe in a vertical direction and the output of thesecond comparator is integrated to grovide a signal representing achanging which is applied to t e reference circuit and to a levelcircuit generating the set level.

8. Apparatus as claimed in claim 6 in which the set level is given by 9.Apparatus as claimed in claim 4 in which the reference circuit issupplied with co-ordinates of aircraft position 0 representing the angleof the glide slope and D representing the distance from the apparatus atwhich the glide slope intersects the runway and operates to determinethe visual range x (D tan 0)/(sin da tan 6 cos lb).

10. Apparatus as claimed in claim 4 in which the reference circuit issupplied with aircraft altitude h and operates to determine visual rangeat h/sin dz.

1]. Apparatus as claimed in claim 13 in which the means for deriving ameasure of visibility comprise means for computing the fog densityflx)at various ranges x from the instantaneous value of the brightness I andthe integrated brightness L at the instant corresponding to receipt ofreflected radiation from the distance x in accordance with the formula12. Apparatus as claimed in claim 13 having a plurality oftransmitter/receiver units coupled to a central computer.

13. A method of determining visual range in fog comprising the steps oftransmitting a pulsed parallel beam of radiation, detecting theradiation reflected back along the same path by the fog,

integrating the brightness of the detected radiation over a time periodwhich is of the order of several times the pulse length,

and deriving from the magnitude of the integrated brightness a measureof visibility.

l= l k

1. Apparatus for measuring visual range in fog comprising: a transmitterfor transmitting a pulsed parallel beam of radiation; a receiver formeasuring the radiation reflected back along the same path by thE fog;means for determining the mathematical integral of the receivedbrightness at any instant over a time period which period is of theorder of several times the pulse length; and means for deriving from theintegrated brightness a measure of visibility.
 2. Apparatus as claimedin claim 1 wherein the means for deriving a measure of visibilitycomprise means for determining the time taken after transmission of apulse for the integrated brightness to reach a set level.
 3. Apparatusas claimed in claim 2 having a gate coupling the integrating means tothe receiver, a gate control circuit, and a comparator comparing theoutput of the integrating means with the set level and supplying adifference signal to the gate control circuit whereby the controlcircuit closes the gate when the set level is reached and generates anoutput representing the time of gate closure.
 4. Apparatus as claimed inclaim 3 including a second comparator which compares the output of thegate control circuit with a reference signal from a reference circuitwhich is a function of aircraft position and of the elevation angle phiof the line of observation, the output of the second comparator beingapplied to vary phi until the line of observation coincides with theline of sight of the aircraft.
 5. Apparatus as claimed in claim 4 inwhich the transmitter/receiver unit is swingable about a horizontal axisby a servomotor to adjust the angle of elevation, the output of thesecond comparator being applied to the servomotor.
 6. Apparatus asclaimed in claim 2 which the transmitter/receiver unit is mounted toobserve in a vertical direction and the set level is a function of theangle of elevation phi of a desired line of observation.
 7. Apparatus asclaimed in claim 4 in which the transmitter/receiver unit is mounted toobserve in a vertical direction and the output of the second comparatoris integrated to provide a signal representing a changing phi which isapplied to the reference circuit and to a level circuit generating theset level.
 8. Apparatus as claimed in claim 6 in which the set level isgiven by
 9. Apparatus as claimed in claim 4 in which the referencecircuit is supplied with co-ordinates of aircraft position thetarepresenting the angle of the glide slope and D representing thedistance from the apparatus at which the glide slope intersects therunway and operates to determine the visual range x (D tan theta )/(sinphi - tan theta cos phi )
 10. Apparatus as claimed in claim 4 in whichthe reference circuit is supplied with aircraft altitude h and operatesto determine visual range x h/sin phi .
 11. Apparatus as claimed inclaim 13 in which the means for deriving a measure of visibilitycomprise means for computing the fog density f(x) at various ranges xfrom the instantaneous value of the brightness IR and the integratedbrightness LR at the instant corresponding to receipt of reflectedradiation from the distance x in accordance with the formula f(x)(IR)/(ITFmvp -2LR)
 12. Apparatus as claimed in claim 13 having aplurality of transmitter/receiver units coupled to a central computer.13. A method of determining visual range in fog comprising the steps oftransmitting a pulsed parallel beam of radiation, detecting theradiation reflected back along the same path by the fog, integrating thebrightness of the detected radiation over a time period which is of theorder of several times the pulse length, and deriving from the magnitudeof the integrated brightness a measure of visibility.